Per Martin-Löf

Per Erik Rutger Martin- Löf ( born May 8, 1942) is a Swedish mathematical logician and philosopher.

Martin- Löf was 1964-1965 at the Moscow State University student of Andrei Kolmogorov, who supervised his dissertation at the University of Stockholm, 1970 ( Notes on constructive mathematics ). Previously, he was in 1968/69 already an assistant professor at the University of Chicago whose Curry Howard isomorphism was later one of the foundations of Martin- Löf 's type theory with William Alvin Howard. Martin- Löf is a professor of mathematics and philosophy at the University of Stockholm.

During his time in Moscow he also refined the notion of random sequence. In 1971, he led his intuitionistic type theory (also called Martin- Löf type theory or constructive type theory ), which, however, he repeatedly reshaped since the first approaches that the "System F " by Jean -Yves Girard generalized, were inconsistent, because one of Girard discovered the paradox. A set of computer -based proof systems such as Nuprl, LEGO, Coq, ALF, Agda, Epigram and Twelf is based on Löf 's type theory. Later, he turned increasingly to philosophical questions of logic.

Martin- Löf also looked at statistics, for example, with the exponential family, the EM algorithm, the problem of missing data in statistics, statistical models, probability semigroups. Among his students is one of the statisticians Rolf Sundberg.

Martin- Löf is a member of the Royal Swedish Academy of Sciences. In 2006 he was Lecturer Godel ( The two layers of logic ), 2012 he held the Tarski Lectures.

He is the brother of the statistician and physicist Anders Martin- Löf ( born 1940 ), professor of actuarial science in Stockholm.

Martin- Löf is a passionate ornithologist and published in 1961 a work, to conclude from the findings of ringed birds on their mortality.

Writings

  • Intuitionistic Type Theory, Bibliopolis, Naples 1984
  • On the Meanings of the Logical Constants and the Justifications of the Logical Laws, Lectures, University of Siena in 1983
  • Statistics from the point of view of statistical mechanics, Lecture, Mathematical Institute, University of Aarhus 1966
  • Notes on constructive mathematics, Almqvist & Wiksell, Stockholm 1970
  • The continuity theorem on a locally compact group, Teor. Verojatnost. i Primenen, Volume 10, 1965, pp. 367-371.
  • Probability theory on discrete semi- groups, Journal of Probability Theory and Related Fields, Volume 4, 1965, pp. 78-102
  • Exact tests, confidence regions and estimates, Proceedings of Conference on Foundational Questions in Statistical Inference ( Aarhus, 1973 ), pp. 121-138, Memoirs, No. 1, Dept.. Theoret. Statist. , Inst Math, Univ. Aarhus, Aarhus, 1974.
  • Constructive mathematics and computer programming, in Cohen (Editor): Logic, Methodology and the Philosophy of Science VI, North Holland 1982, p 153-175
Curry–Howard correspondence Jean-Yves Girard Expectation–maximization algorithm Integrated Authority File
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